Abstract
The knowledge of speed and direction of coastal ocean currents are critical for carrying out search and rescue at sea, to respond to the hazardous marine oil spills, to estimate the dispersal pattern of pollutants, to issue warnings against tsunamis and cyclones etc. Such operations need uninterrupted observational data of sea surface currents over wide area with high spatial and temporal resolution. The High frequency (HF) radars installed at the shore, sense the surface of ocean using electromagnetic waves, and provide the speed and direction of ocean currents over a specific spatial domain at high temporal resolution. However, the frequent gaps in the data are a concern for its usage. The gaps arise due to its dependence on the roughness of the sea other electromagnetic interferences from environment sources and due to data acquisition failures. Hence, it is necessary to fill the gaps for successful usage of HF radar data. The present work describes a method to fill the gaps in the HF radar data using complex empirical orthogonal functions (CEOF). Before filling the missing data, HF radar data is assessed with available observations. The CEOFs are calculated iteratively using singular value decomposition. The number of statistically significant CEOFs required to construct the missing HF radar currents data accurately along the Indian coast are obtained through a cross-validation procedure. The proposed method is first validated for various rates of synthetic data gaps created in synthetic data and in model derived cyclonic wind fields and comparisons are illustrated, the reconstructed data and the original data are in good match
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References
Alvera-Azcárate, A., Barth, A., Sirjacobs, D., & Beckers, J.-M. (2009). Enhancing temporal correlations in EOF expansions for the reconstruction of missing data using DINEOF. Ocean Science, 5, 475–485. https://doi.org/10.5194/os-5-475-2009.
Alvera-Azcárate, A., Barth, A., Sirjacobs, D., Lenartz, F., & Beckers, J. M. (2011). Data interpolating empirical orthogonal functions (DINEOF): A tool for geophysical data analyses. Mediterranean Marine Science, 12(2011), 5–11. https://doi.org/10.12681/mms.64.
Arunraj, K. S., Jena, B. K., Suseentharan, V., & Rajkumar, J. (2018). Variability in Eddy distribution associated with east india coastal current from high-frequency radar observations along southeast coast of India. Journal of Geophysical Research: Oceans, 123, 2018JC014041. https://doi.org/10.1029/2018jc014041.
Balas, C. E., Koç, L., & Balas, L. (2004). Predictions of missing wave data by recurrent neuronets. Journal of Waterway, Port, Coastal, Ocean Engineering, 130, 256–265. https://doi.org/10.1061/(ASCE)0733-950X(2004)130:5(256).
Barrick, D. E. (1978). HF radio oceanography—A review. Boundary-Layer Meteorology, 13, 23–43. https://doi.org/10.1007/BF00913860.
Barrick, D. E. (1979). A coastal radar system for tsunami warning. Remote Sensing of Environment, 8, 353–358. https://doi.org/10.1016/0034-4257(79)90034-8.
Barrick, D. E., Evans, M. W., & Weber, B. L. (1977). Ocean surface currents mapped by radar. Science (80-.), 198, 138–144. https://doi.org/10.1126/science.198.4313.138.
Barrick, D. E., & Lipa, B. J. (1979a). Ocean surface features observed by HF coastal ground-wave radars: A progress review. Ocean wave climate (pp. 129–152). Boston, MA: Springer US. https://doi.org/10.1007/978-1-4684-3399-9_6.
Barrick, D. E., & Lipa, B. J. (1979b). A compact transportable HF radar system for directional coastal wave field measurements. Ocean wave climate (pp. 153–201). Boston, MA: Springer US.
Batista, G., & Monard, M. C. (2002). A study of K-nearest neighbour as an imputation method, HIS. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.14.3558. Accessed 25 Apr 2019.
Beckers, J. M., & Rixen, M. (2003). EOF calculations and data filling from incomplete oceanographic datasets. Journal of Atmospheric and Oceanic Technology, 20, 1839–1856. https://doi.org/10.1175/1520-426(2003)020%3c1839:ECADFF%3e2.0.CO;2.
Bellomo, L., Griffa, A., Cosoli, S., Falco, P., Gerin, R., Iermano, I., et al. (2015). Toward an integrated HF radar network in the Mediterranean Sea to improve search and rescue and oil spill response: The TOSCA project experience. Journal of Operational Oceanography, 8(2), 95–107. https://doi.org/10.1080/1755876X.2015.1087184.
Bennis, S., Berrada, F., & Kang, N. (1997). Improving single-variable and multivariable techniques for estimating missing hydrological data. Journal of Hydrology, 191, 87–105. https://doi.org/10.1016/S0022-1694(96)03076-4.
Brink, K. H., & Muench, R. D. (1986). Circulation in the point conception-Santa Barbara channel region. Journal of Geophysical Research, 91, 877. https://doi.org/10.1029/JC091iC01p00877.
Chapman, R. D., Shay, L. K., Graber, H. C., Edson, J. B., Karachintsev, A., Trump, C. L., et al. (1997). On the accuracy of HF radar surface current measurements: Intercomparisons with ship-based sensors. Journal of Geophysics Research Ocean, 102, 18737–18748. https://doi.org/10.1029/97JC00049.
Crombie, D. D. (1955). Doppler spectrum of sea echo at 13.56 Mc/s. Nature., 175, 681–682. https://doi.org/10.1038/175681a0.
Crombie, D. D., & Watts, J. M. (1968). Observations of coherent backscatter of 2–10 MHz radio surface waves from the sea. Deep Sea Research Oceanography Abstract, 15(1968), 81–87. https://doi.org/10.1016/0011-7471(68)90029-6.
Elshorbagy, A., Simonovic, S. P., & Panu, U. S. (2002). Estimation of missing streamflow data using principles of chaos theory. Journal of Hydrology, 255, 123–133. https://doi.org/10.1016/S0022-1694(01)00513-3.
Emery, B. M., Washburn, L., & Harlan, J. A. (2004). Evaluating radial current measurements from CODAR high-frequency radars with moored current meters. Journal of Atmospheric and Oceanic Technology, 21, 1259–1271. https://doi.org/10.1175/1520-0426(2004)021%3c1259:ERCMFC%3e2.0.CO;2.
Forget, P. (2015). Noise properties of HF radar measurement of ocean surface currents. Radio Science, 50(2015), 764–777. https://doi.org/10.1002/2015RS005681.
Fredj, E., Roarty, H., Kohut, J., Smith, M., & Glenn, S. (2016). Gap filling of the coastal ocean surface currents from HFR data: Application to the mid-atlantic bight HFR net. Journal of Atmospheric and Oceanic Technology, 33(2016), 1097–1111. https://doi.org/10.1175/JTECH-D-15-0056.1.
Gauci, A., Drago, A., & Abela, J. (2016). Gap filling of the CALYPSO HF radar sea surface current data through past measurements and satellite wind observations. International Journal of Navigation and Observation, 2016(2016), 1–9. https://doi.org/10.1155/2016/2605198.
Golub, G. H., & Van Loan, C. F. (2013). Matrix computations. Johns Hopkins Univ Press, 2013. https://books.google.co.in/books?hl=en&lr=&id=5U-l8U3P-UC&oi=fnd&pg=PT10&dq=Matrix+Computation,+G.+H.+Golub&ots=7_GBKo2Nbr&sig=xuVmCVW4eIXplnVE58PL8-19FRE#v=onepage&q=MatrixComputation%2CG.H.Golub&f=false. Accessed 25 Apr 2019.
Graham, J. W. (2009). Missing data analysis: Making it work in the real world. Annual Review of Psychology, 60(2009), 549–576. https://doi.org/10.1146/annurev.psych.58.110405.085530.
Gurgel, K. W. (1994). Shipborne measurement of surface current fields by HF radar. In Proceeding oceanic IEEE (pp. III/23–III/27). https://doi.org/10.1109/oceans.1994.364167.
Gurgel, K. W., Essen, H. H., & Kingsley, S. P. (1999). High-frequency radars: Physical limitations and recent developments. Coastal Engineering, 37, 201–218. https://doi.org/10.1016/S0378-3839(99)00026-5.
Hannachi, A., Jolliffe, I. T., & Stephenson, D. B. (2007). Empirical orthogonal functions and related techniques in atmospheric science: A review. International Journal of Climatology, 27, 1119–1152. https://doi.org/10.1002/joc.1499.
Hardy, D. M., & Walton, J. J. (1978). Principal components analysis of vector wind measurements. Journal of Applied Meteorology, 17, 1153–1162. https://doi.org/10.2307/26178591.
Henn, B., Raleigh, M. S., Fisher, A., & Lundquist, J. D. (2012). A comparison of methods for filling gaps in hourly near-surface air temperature data. Journal of Hydrometeorology, 14, 929–945. https://doi.org/10.1175/jhm-d-12-027.1.
Hernández-Carrasco, I., Solabarrieta, L., Rubio, A., Esnaola, G., Reyes, E., & Orfila, A. (2018). Impact of HF radar current gap-filling methodologies on the Lagrangian assessment of coastal dynamics. Ocean Science, 14(4), 827–847. https://doi.org/10.5194/os-14-827-2018.
Heron, M., Gomez, R., Weber, B., Dzvonkovskaya, A., Helzel, T., Thomas, N., et al. (2016). Application of HF Radar in hazard management. International Journal of Antennas Propagation. https://doi.org/10.1155/2016/4725407.
Hodgins, D. O. (1992). The seasonde high-freqency radar system for surface current measurements, Proc. ASEAN Sci. Technol. Week. http://www.codar.com/images/about/1992Hodgins_ASEAN.pdf. Accessed 30 Apr 2019.
Houseago-Stokes, R. E., & Challenor, P. G. (2004). Using PPCA to estimate EOFs in the presence of missing values. Journal of Atmospheric and Oceanic Technology, 21, 1471–1480. https://doi.org/10.1175/1520-0426(2004)021%3c1471:UPTEEI%3e2.0.CO;2.
Jena, B. K., Anuraj, K. S., Suseentharan, V., Tushar, Kukadiya, & Karthikeyan, T. (2019). Indian coastal ocean radar network. Current Science, 116(3), 372–378.
Jouini, M., Lévy, M., Crépon, M., & Thiria, S. (2013). Reconstruction of satellite chlorophyll images under heavy cloud coverage using a neural classification method. Remote Sensors Environment, 131, 232–246. https://doi.org/10.1016/j.rse.2012.11.025.
Kalra, R., & Deo, M. C. (2007). Genetic programming for retrieving missing information in wave records along the west coast of India. Applied Ocean Research, 29(2007), 99–111. https://doi.org/10.1016/J.APOR.2007.11.002.
Kaplan, D. M., Largier, J., & Botsford, L. W. (2005). HF radar observations of surface circulation off Bodega Bay (northern California, USA). Journal of Geophysical Research, 110, C10020. https://doi.org/10.1029/2005JC002959.
Kaplan, D. M., & Lekien, F. (2007). Spatial interpolation and filtering of surface current data based on open-boundary modal analysis. Journal of Geophysical Research, 112, C12007. https://doi.org/10.1029/2006JC003984.
Kim, S. Y., Terrill, E. J., & Cornuelle, B. D. (2008). Mapping surface currents from HF radar radial velocity measurements using optimal interpolation. Journal of Geophysical Research, 113, C10023. https://doi.org/10.1029/2007JC004244.
Kohut, J., Glenn, S., & Barrick, D. (1999). SeaSonde is integral to coastal flow model development. Hydro International 3, 32–35. https://www.sciencebase.gov/catalog/item/5053e854e4b097cd4fcf6010. Accessed 25 April 2019.
Kokkini, Z., Potiris, M., Kalampokis, A., & Zervakis, V. (2014). HF Radar observations of the dardanelles outflow current in the north eastern Aegean using validated WERA HF radar data. Mediterranean Marine Science, 15(4), 753–768. https://doi.org/10.12681/mms.938.
Krasnopolsky, V., Nadiga, S., Mehra, A., Bayler, E., & Behringer, D. (2016). Neural networks technique for filling gaps in satellite measurements: Application to ocean color observations. Computational Intelligence and Neuroscience, 2016, 1–9. https://doi.org/10.1155/2016/6156513.
Lana, A., Marmain, J., Fernández, V., Tintoré, J., & Orfila, A. (2016). Wind influence on surface current variability in the Ibiza Channel from HF Radar. Ocean Dynamics, 66, 483–497. https://doi.org/10.1007/s10236-016-0929-z.
Lipa, B. J., & Barrick, D. E. (1983). Least-squares methods for the extraction of surface currents from CODAR crossed-loop data: Application at ARSLOE. IEEE Journal of Oceanic Engineering, 8(1983), 226–253. https://doi.org/10.1109/JOE.1983.1145578.
Lipa, B., Barrick, D., Diposaptono, S., Isaacson, J., Jena, B. K., Nyden, B., et al. (2012). High frequency (HF) radar detection of the weak 2012 Indonesian tsunamis. Remote Sensors, 4, 2944–2956. https://doi.org/10.3390/rs4102944.
Liu, Y., Kerkering, H., & Weisberg, R. H. (2015). Coastal ocean observing systems. New York: Academic Press.
Maidment, D. R. (1993). Handbook of hydrology. New York: McGraw-Hill.
Mukhopadhyay, S., Shankar, D., Aparna, S. G., & Mukherjee, A. (2017). Observations of the sub-inertial, near-surface East India Coastal Current. Continental Shelf Research, 148(2017), 159–177. https://doi.org/10.1016/J.CSR.2017.08.020.
Orfila, A., Molcard, A., Sayol, J. M., Marmain, J., Bellomo, L., Quentin, C., et al. (2015). Empirical forecasting of HF-radar velocity using genetic algorithms. IEEE Transactions on Geoscience and Remote Sensing, 53(5), 2875–2886. https://doi.org/10.1109/TGRS.2014.2366294.
Paduan, J. D., & Washburn, L. (2013). High-frequency radar observations of ocean surface currents. Annual Review of Marine Science, 5(2013), 115–136. https://doi.org/10.1146/annurev-marine-121211-172315.
Pappas, C., Papalexiou, S. M., & Koutsoyiannis, D. (2014). A quick gap filling of missing hydrometeorological data. Journal of Geophysical Research, 119, 9290–9300. https://doi.org/10.1002/2014JD021633.
Pashova, L., Koprinkova-Hristova, P., & Popova, S. (2013). Gap filling of daily sea levels by artificial neural networks. TransNav, International Journal on Marine Navigation and Safety od Sea Transportation, 7, 225–232. https://doi.org/10.12716/1001.07.02.10.
Pisoni, E., Pastor, F., & Volta, M. (2008). Artificial Neural Networks to reconstruct incomplete satellite data: Application to the Mediterranean Sea Surface Temperature. Nonlinear Process Geophysics, 15, 61–70. https://doi.org/10.5194/npg-15-61-2008.
Pond, S., & Pickard, G. L. (2008). Introductory dynamical oceanography, 2nd edn, 2013. https://doi.org/10.1016/c2009-0-24288-7.
Powers, J. G., Klemp, J. B., Skamarock, W. C., Davis, C. A., Dudhia, J., Gill, D. O., et al. (2017). The weather research and forecasting model: Overview, system efforts, and future directions. Bulletin of the American Meteorological Society, 98, 1717–1737. https://doi.org/10.1175/BAMS-D-15-00308.1.
Saha, D., Deo, M. C., & Bhargava, K. (2016). Interpolation of the gaps in current maps generated by high-frequency radar. International Journal of Remote Sensing, 37(2016), 5135–5154. https://doi.org/10.1080/01431161.2016.1230281.
Saikumar, P. J., & Ramashri, T. (2017). Impact of physics parameterization schemes in the simulation of laila cyclone using the advanced mesoscale weather research and forecasting model. International Journal of Applied Engineering Research, 12, 12645–12651. https://doi.org/10.14419/ijet.v7i3.29.18809.
Schott, F. A., Xie, S.-P., & McCreary, J. P., Jr. (2009). Indian Ocean circulation and climate variability. Reviews of Geophysics, 47(2009), 1–46. https://doi.org/10.1029/2007RG000245.1.INTRODUCTION.
Shankar, D., McCreary, J. P., Han, W., & Shetye, S. R. (1996). Dynamics of the East India Coastal Current: 1. Analytic solutions forced by interior Ekman pumping and local alongshore winds. Journal of Geophysics Research Ocean, 101(1996), 13975–13991. https://doi.org/10.1029/96jc00559.
Shankar, D., Vinayachandran, P. N., & Unnikrishnan, A. S. (2002). The monsoon currents in the north Indian Ocean. Progress in Oceanography, 52, 63–120. https://doi.org/10.1016/S0079-6611(02)00024-1.
Stewart, R. H., & Joy, J. W. (1974). HF radio measurements of surface currents, Deep Sea. Research Oceanography Abstract, 21, 1039–1049. https://doi.org/10.1016/0011-7471(74)90066-7.
Sturges, W. (1983). On interpolating gappy records for time-series analysis. Journal of Geophysical Research, 88, 9736–9740. https://doi.org/10.1029/JC088iC14p09736.
Taylor, M. H., Losch, M., Wenzel, M., & Schröter, J. (2013). On the sensitivity of field reconstruction and prediction using empirical orthogonal functions derived from Gappy data. Journal of Climate, 26, 9194–9205. https://doi.org/10.1175/JCLI-D-13-00089.1.
Thomson, R. E., & Emery, W. J. (2014). Data analysis methods in physical oceanography, 3rd edn, 2014. https://doi.org/10.1016/c2010-0-66362-0.
Tutz, G., & Ramzan, S. (2015). Improved methods for the imputation of missing data by nearest neighbor methods. Computational Statistics and Data Analysis, 90, 84–99. https://doi.org/10.1016/j.csda.2015.04.009.
Ustoorikar, K., & Deo, M. C. (2008). Filling up gaps in wave data with genetic programming. Marine Structures, 21, 177–195. https://doi.org/10.1016/J.MARSTRUC.2007.12.001.
Wenzel, M., & Schröter, J. (2010). Reconstruction of regional mean sea level anomalies from tide gauges using neural networks. Journal of Geophysical Research, 115, C08013. https://doi.org/10.1029/2009JC005630.
Yaremchuk, M., & Sentchev, A. (2011). A combined EOF/variational approach for mapping radar-derived sea surface currents. Continental Shelf Research, 31(2011), 758–768. https://doi.org/10.1016/J.CSR.2011.01.009.
Acknowledgements
Authors would like to express their sincere and heartfelt thanks to Dr. Arya Paul, INCOIS for introducing Complex Empirical Orthogonal Functions. We also thank NIOT for maintaining HF radars and ensuring the data transmission. We thank anonymous reviewers for their valuable suggestions and comments, which improved the quality of manuscript. The HF radar data used in this study is accessible at http://odis.incois.gov.in/index.php/insitu-data/coastal-hf-radar/data-access on request. This is INCOIS contribution number—396.
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Kolukula, S.S., Baduru, B., Murty, P.L.N. et al. Gaps Filling in HF Radar Sea Surface Current Data Using Complex Empirical Orthogonal Functions. Pure Appl. Geophys. 177, 5969–5992 (2020). https://doi.org/10.1007/s00024-020-02613-x
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DOI: https://doi.org/10.1007/s00024-020-02613-x